Submodular Minimization via Pathwidth

Nagamochi, Hiroshi

doi:10.1007/978-3-642-29952-0_54

Cited by 1 publication

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“…More interestingly, although the submodularity of function Γ + G is used to derive the upper bound O(n k ), the mechanism of the algorithm is self-contained in the sense that it never relies on any other optimization mechanism such as submodular minimization and dynamic programming to attain the nontrivial upper bound. In fact, recently Nagamochi [13] proved that the new mechanism can be conversely used to solve the submodular minimization problem, the most representative optimization problem.…”

Section: Introductionmentioning

confidence: 99%

Linear Layouts in Submodular Systems

Nagamochi

2012

Algorithms and Computation

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Linear layout of graphs/digraphs is one of the classical and important optimization problems that have many practical applications. Recently Tamaki proposed an O(mn k+1 )-time and O(n k )-space algorithm for testing whether the pathwidth (or vertex separation) of a given digraph with n vertices and m edges is at most k. In this paper, we show that linear layout of digraphs with an objective function such as cutwidth, minimum linear arrangement, vertex separation (or pathwidth) and sum cut can be formulated as a linear layout problem on a submodular system (V, f ) and then propose a simple framework of search tree algorithms for finding a linear layout (a sequence of V ) with a bounded width that minimizes a given cost function. According to our framework, we obtain an O(kmn 2k )-time and O(n + m)-space algorithm for testing whether the pathwidth of a given digraph is at most k.

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Section: Introductionmentioning

confidence: 99%